The adaptive food-web hypothesis suggests that an adaptive foraging switch inverses the classically negative complexity-stability relationships of food webs into positive ones, providing a possible resolution for the long-standing paradox of how populations persist in a complex natural food web. However, its applicability to natural ecosystems has been questioned, because the positive relationship does not emerge when a niche model, a realistic "benchmark" of food-web models, is used. I hypothesize that, in the niche model, increasing connectance influences the fraction of basal species to destabilize the system and this masks the inversion of the negative complexity-stability relationship in the presence of adaptive foraging. A model analysis shows that, if this confounding effect is eliminated, then, even in a niche model, a population is more likely to persist in a more complex food web. This result supports the robustness of adaptive food-web hypothesis and reveals the condition in which the hypothesis should be tested.